Question

what is the value of x?
$x =$
$(4x)^{circ}$
$(3x + 85)^{circ}$
$(3x + 25)^{circ}$

Explanation:

Step1: Apply the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
So, \(4x+(3x + 25)=3x + 85\)

Step2: Simplify the equation

First, expand the left - hand side: \(4x+3x + 25=3x + 85\).
Combine like terms on the left: \(7x+25 = 3x+85\).
Subtract \(3x\) from both sides: \(7x-3x+25=3x-3x + 85\), which gives \(4x+25=85\).
Subtract \(25\) from both sides: \(4x+25 - 25=85 - 25\), so \(4x=60\).

Step3: Solve for \(x\)

Divide both sides by \(4\): \(x=\frac{60}{4}\)

Answer:

\(15\)